Topology of the Yang-Mills Configuration space

It will be described how to uniquely fix the gauge using Coulomb gauge fixing, avoiding the problem of Gribov copies. The fundamental modular domain, which represents a one-to-one representation of the set of gauge invariant degrees of freedom, is a bounded convex subset of the trans- verse gauge fields. Boundary identifications are the only remnants of the Gribov copies, and carry all the information about the topology of the Yang-Mills configuration space. Conversely, the known topology can be shown to imply that (on a set of measure zero on the boundary) some points of the boundary coincide with the Gribov horizon. For the low-lying energies, wavefunctionals can be shown to spread out "across" certain parts of these boundaries. This is how the topology of Yang-Mills configuration space has an essential influence on the low-lying spectrum, in a situation where these non- perturbative effects are not exponentially suppressed. This write-up is a short summary, with adequate references, where details on most of the material I have presented can be found. However, not published before, is a new observation concerning Henyey's gauge copies.